Question

the diagram below shows a solution with one solute. the solution fills a closed container that is divided by a membrane. the membrane is permeable to the solute particles. 1 ml 2 ml the volume on the left is half the volume on the right. which of the following statements describes how the solution will change over time? for the solute particles to reach equilibrium, more particles will move across the membrane from the right to the left. for the solute particles to reach equilibrium, more particles will move across the membrane from the left to the right. because the solute particles have reached equilibrium, the same number of particles will move across the membrane in each direction.

Explanation:

Step1: Calculate initial concentrations

Concentration is calculated as the number of solute particles divided by volume.
Let's assume the number of particles on the left is \(n_1 = 2\) and on the right is \(n_2=8\).
Concentration on the left \(C_1=\frac{n_1}{V_1}=\frac{2}{1\mathrm{mL}} = 2\mathrm{particles/mL}\)
Concentration on the right \(C_2=\frac{n_2}{V_2}=\frac{8}{2\mathrm{mL}}=4\mathrm{particles/mL}\)

Step2: Determine the direction of particle movement

Particles move from an area of higher concentration to an area of lower concentration.
Since \(C_2 > C_1\), more particles will move from the right (higher - concentration side) to the left (lower - concentration side) until equilibrium is reached. At equilibrium, the concentration on both sides will be equal. Let the final number of particles on the left be \(x\) and on the right be \(y\), and \(x + y=10\) (total number of particles) and \(\frac{x}{1\mathrm{mL}}=\frac{y}{2\mathrm{mL}}\), solving \(y = 2x\) and substituting into \(x + y=10\) gives \(x=\frac{10}{3}\approx3.33\) and \(y=\frac{20}{3}\approx6.67\)

Answer:

For the solute particles to reach equilibrium, more particles will move across the membrane from the right to the left.